/** * Supply chain coordination problem * OPL model for a leaf agent, i.e. an agent that has no sub-suppliers. * The agent agrees delivery schedules for its products with other agents in the problem. * The products of this agent are the components of the receiving agents. */ /** * MODEL INPUT PARAMETERS */ // Time horizon int numPeriods = ...; range horizon 1..numPeriods; // Number of product configurations int numProducts = ...; range products 1..numProducts; // Number of components int numComponents = ...; range components 1..numComponents; // Maximum number of orders to consider for each product int maxNumOrders[products] = ...; // Bill Of Materials int bom[products,components] = ...; // The batch size of a product in a particularly delivery int batchSize[products] = ...; // The lead time/delivery time for a particular component // I.e. the number of periods between an order being made // and the goods being delivered int leadtime[products] = ...; // Number of processing cycles for each configuration int cycles[products]= ...; // Number of cycles required to setup a configuration int setupCycles[products] = ...; // Factory capacity int capacity[horizon] = ...; // Starting product inventory int openingProductInventory[products] = ...; // Starting component inventory int openingComponentInventory[components] = ...; // Holding costs int productHoldingCost[products] = ...; int componentHoldingCost[components] = ...; // Setup costs int setupCosts[products] = ...; // Expected inventory arriving for each component in the time horizon int componentArrivals[horizon,components] = ...; // Constants int maxManufacture = max(t in horizon) capacity[t]; int maxOrders = max(p in products) maxNumOrders[p]; /** * PUBLIC VARIABLES * (variables constrained with other agents) */ // The number of orders for a each product to be delivered in each period. var int productDeliverySchedule[products,horizon] = 0..maxOrders; /** * PRIVATE VARIABLES * (variables not constrained with other agents) */ // 0/1 variable indicating whether or not a product will be built in a particular period var int isbuilt[horizon,products] in 0..1; // The number of a product built in a particular period var int manufacture[horizon,products] in 0..maxManufacture; /** * AUXILIARY VARIABLES * (additional variables used to simplify the model specification) */ // Remaining product inventory after each period var float+ productInventory[0..numPeriods,products]; // Remaining component inventory after each period var float+ componentInventory[0..numPeriods,components]; // The quantity of product delivered in each period var float+ deliveryQuantity[horizon, products]; // Components needed on a particular day to produce everything in manufacture var float+ componentsUsed[horizon, components]; minimize // Total cost sum (t in horizon, p in products) ( (productHoldingCost[p]*productInventory[t,p]) + (isbuilt[t,p]*setupCosts[p]) ) + sum (t in horizon, c in components) ( (componentHoldingCost[c]*componentInventory[t,c]) ) subject to { // Opening product inventory forall(p in products) productInventory[0,p]=openingProductInventory[p]; // Opening component inventory forall(c in components) componentInventory[0,c]=openingComponentInventory[c]; // Calculate the number of products delivered forall(p in products) forall (t in 1..numPeriods-leadtime[p]) deliveryQuantity[t,p] = batchSize[p] * productDeliverySchedule[p,t+leadtime[p]]; forall(p in products) forall (t in [numPeriods-leadtime[p]+1..numPeriods]) deliveryQuantity[t,p] = 0; // Set the isbuilt variable correctly - should be 1 if any of that product is built on that day forall(t in horizon, p in products) maxManufacture * isbuilt[t,p] >= manufacture[t,p]; // Capacity constraint for manufacturing decision // The factory's capacity for each day cannot be exceeded forall(t in horizon) sum(p in products) (manufacture[t,p]*cycles[p] + isbuilt[t,p]*setupCycles[p]) <= capacity[t]; // The number of components needed is calculated by multiplying manufacturing decision by BOM forall(t in horizon, c in components) componentsUsed[t,c] = sum(p in products) manufacture[t,p]*bom[p,c]; // Calculate the expected excess product inventory of each period forall(t in horizon, p in products) productInventory[t,p] = productInventory[t-1,p] + manufacture[t,p] - deliveryQuantity[t,p]; // Calculate the expected excess component inventory of each period forall(t in horizon, c in components) componentInventory[t,c] = componentInventory[t-1,c] + componentArrivals[t,c] - componentsUsed[t,c]; };